Detrending Multi-Subject, Multilevel, Short Time Series Data

Trends represent systematic intra-individual variations that occur over slower time scales that, if unaccounted, are known to yield biases in estimation of momentary change patterns captured by time series models. The applicability of detrending methods have been rarely assessed when involving multi-level longitudinal panel data with relatively few measurements and nested structures. This paper evaluated the efficacy of various detrending methods against a single-stage Bayesian approach in extracting intra- and inter-individual change information from multi-level non-linear growth curve models with autoregressive residuals (ml-GAR), where random effects are present in both the growth and autoregressive (AR) processes. A Monte Carlo simulation study revealed that the single-stage Bayesian approach exhibited satisfactory properties with as few as five time points, whereas two-stage approaches still yielded relatively substantial biases in the parameters for the AR model that did not improve with increased number of subjects, even when detrending was performed with the correctly specified trend model. Empirical results from the Early Childhood Longitudinal Study—Kindergarten Class (ECLS-K) data suggested substantial deviations in conclusions regarding children’s reading ability using two-stage in comparison to single-stage approaches for fitting the ml-GAR, thus highlighting the importance of simultaneous modeling of trends and intraindividual variability whenever feasible.